Many of my friends here in Israel support organisations like Breaking the Silence. This is not unusual. Of course, being citizens we cannot be refused entry and we generally whiz through passport check without any hinderance.
I suspect being active in the BDS circles might earn you thorough questioning, but who knows? Much like any border police, the Israeli authorities don't share their profiling rules, but if you just cooperate and you're not up for anything too subversive, you'll be out of the airport in no time.
For a personal edge, some of my friends and Couchsurfing guests shared stories with me. Here's the most extreme one:
A young Swiss citizen, whose father was born in the West Bank. Traveling with his girlfriend, Though his family has long
moved to Switzerland, where he was born, the passport control stopped him for
questioning. In the meanwhile, his girlfriend was permitted entry
instantly, as would be expected for a holder of a Swiss passport, and
had to wait for him. Finally, the officer pulled up his
father's ID and photo on the computer screen (yeah, modern governments
scare me too), and upon confirming his identity, permitted his
The whole experience was obviously unpleasant and distressing to my guests, but I think overall they've enjoyed their trip.
If you're interested in more horror stories, you can find some here (note, this is an Israeli publication -- we do openly discuss such issues around here). Take it with a grain of salt; journalism is naturally sensationalistic. ("Man bitten by a dog" is not news, "Dog bitten by a man" is.) I'm sure you've heard about people being questioned by the US border police as well, yet it doesn't deter most people from travelling to the US.
It's best to be smart about it. There's no need to discuss your West Bank travel plans with the officer, especially if your plans include something as mundane as visiting churches in Bethlehem and snapping photos of the wall. Do not joke about bombs, do not get into political arguments, apply the same common sense as with any other border police officer around the world.